# MATHEMATICS 2 - 2020/1

Module code: ENG1065

Module Overview

Engineers frequently use mathematical models, and in particular differential equations in one or more variables and matrices are common in this context. This is a further first level engineering mathematics module designed to support teaching in other engineering science modules by introducing students to concepts and solution methods in these areas. Statistics and probability also play a significant role in the assessment of real-life engineering problems and an introduction to key concepts in this area is also included

Module provider

Mechanical Engineering Sciences

Module Leader

ROCKLIFF Nicole (Mech Eng Sci)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 4

JACs code: G100

Module cap (Maximum number of students): N/A

Module Availability

Semester 2

Prerequisites / Co-requisites

ENG1061 Mathematics 1

Module content

Indicative content includes:

- Functions of several variables: Partial derivatives for functions of several variables, total derivative, application to small changes in a function and errors. Extrema of functions of two variables. Simple double integrals. Simple vector functions of several variables and basic vector calculus- grad, div and curl
- Ordinary differential equations: First order, first degree ODE's of separable type and the integrating factor method. Second order ODE's with constant coefficients (complementary solution and particular integrals). Initial and boundary value problems.
- Matrices, determinants, eigenvalues: Matrix addition, multiplication, etc., determinants, Cramer's rule. Matrix operations involving transpose, inverse, rank of matrix. Solving systems of equations using matrices, esp. Gaussian elimination. Eigenvalues and eigenvectors; applications to systems of linear differential equations and normal modes.
- Partial differential equations Introduction to PDE's, separation of variables method using trial solution.
- Probability and statistics: Descriptive statistics: numerical (mean, mode, median, variance etc).. Basic Probability: elementary laws, random variables, mean and variance. Probability distributions: Discrete probability distributions (binomial, Poisson); continuous probability distributions (normal).

Assessment pattern

Assessment type | Unit of assessment | Weighting |
---|---|---|

Examination | EXAMINATION - 2 HOURS | 80 |

Coursework | COURSEWORK | 20 |

Alternative Assessment

N/A

Assessment Strategy

The __assessment strategy__ is designed to provide students with the opportunity to demonstrate their ability to recognise problem types, select appropriate solution methods and carry out various solution techniques.

Thus, the __summative assessment__ for this module consists of:

- One piece of coursework covering the full breadth of topics and techniques taught in the first part of the semester, with examples to not only cover ‘standard’ problems but also some modelling.

Learning outcomes 1,2,3 20% 12 hrs

- One two-hour examination with problems on topics from across the whole syllabus but inevitably in the time not covering every technique/concept and with some weighting on those areas from later in the module

Learning outcomes 1,2 ,4-8 80% 2 hrs

__Formative assessment and feedback__

Formative ‘assessment’ is a regular ongoing process all semester through work on the tutorial questions. Formative feedback is provided orally on a one-to-one basis and to the whole group in tutorial/problems classes, and through the issue using the VLE of selected samples of fully worked solutions to tutorial problems.

The summative assessment is also formative, with individual comments on performance being returned along with scripts and also with overview comments posted on the VLE.

Module aims

- Further understanding and knowledge of mathematical and statistical concepts and techniques
- Skills in the selection and implementation of mathematical techniques to engineering problems
- An appreciation of the importance of mathematical modelling of physical problems and the interpretation of mathematical results.

Learning outcomes

Attributes Developed | Ref | ||
---|---|---|---|

001 | UK_SPEC Learning Outcome codes: SM2b,SM2m, EA3b, , G1 On successful completion of this module, students will be able to: select and apply appropriate techniques of differential and integral calculus to engineering problems; | KC | |

002 | Solve straightforward ordinary differential equations as encountered in engineering problems; | KCP | |

003 | Discuss the role of mathematical modelling and be able to produce and explain simple mathematical models of physical problems; | CPT | |

004 | Solve typical engineering-related second order partial differential equations; | KC | |

005 | Manipulate matrices in appropriate contexts and use matrix methods to solve sets of linear algebraic equations; | KC | |

006 | Determine matrix eigenvalues and eigenvectors, use to solve engineering systems modelled by differential equations and relate the results to characteristics of the physical system; | KCP | |

007 | Present and summarise simple statistical data graphically and numerically; | KCPT | |

008 | Recognise appropriate probability distributions and use them to calculate probabilities and apply to e.g. simple ideas of quality control. | KCP |

Attributes Developed

**C** - Cognitive/analytical

**K** - Subject knowledge

**T** - Transferable skills

**P** - Professional/Practical skills

Overall student workload

Independent Study Hours: 95

Lecture Hours: 44

Tutorial Hours: 11

Methods of Teaching / Learning

The __learning and teaching__ strategy is designed to familiarise students with mathematical concepts and techniques, supported by extensive use of examples and applications, in which students themselves are engaged in both lectures and, more extensively, in tutorials/problems classes.

The __learning and teaching__ methods include:

- Lectures (4 hrs/wk, for 11 weeks) to introduce new concepts and techniques and provide illustrative examples and applications; students are engaged with performance of examples, questioning on concept and observations.
- Recommended wider reading of matching sections of relevant recommended texts.
- Problem sheets of examples for technique selection and skill development.
- Tutorials/problems classes (1 hr/wk for 11 weeks) with staff and PG assistance for the development of skills in technique application and also in selection of appropriate techniques, using the above problems sheets; assistance is given both at individual level, and for the group on common areas of difficulty
- Coursework (summative but also formative) to assess technique selection and skill development and also elements of modelling and intepration of physical problems
- Examination

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Programmes this module appears in

Programme | Semester | Classification | Qualifying conditions |
---|---|---|---|

Biomedical Engineering BEng (Hons) | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Aerospace Engineering BEng (Hons) | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Aerospace Engineering MEng | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Mechanical Engineering MEng | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Mechanical Engineering BEng (Hons) | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Biomedical Engineering MEng | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Automotive Engineering MEng | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Automotive Engineering BEng (Hons) | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2020/1 academic year.